 Solution

ID: past-exam-of-the-year-2-of-the-earth-sciences-geology-course-of-the-university-of-oxford/2024/paper-3/8/a/iv/solution

The true daily component has

f_{D} = 1 da y^{- 1}

t_{n} = 2 n /3

cos (2 π t_{n}) = cos (4 πn /3) = cos (2 πn /3) .

The last sequence is also produced by a continuous cosine with frequency

0.5 da y^{- 1}

sampled at those same times. Hence the observed peak is the sampled sinusoid alias

f_{alias} = ∣ f_{D} - f_{s} ∣ = 0.5 da y^{- 1} .

It is not evidence for an additional two-day physical temperature cycle.

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